In this project we propose to develop optimal methods for magnetic resonance imaging (MRI). These methods are 'optimal' in the sense that the engineering theory of feedback control is applied in the imaging acquisition strategy in order to extract maximum information for production of stable image estimates. These methods will be applied primarily for dynamic imaging of processes that evolve so rapidly in time that they cannot be adequately resolved both spatially and temporally with suitable volume coverage using current dynamic MRI methods. Our hypothesis is that significant improvement in volume coverage, without loss of image quality or temporal resolution, can be obtained if optimized methods are used. The characterization of the MRI system within the general context of feedback control theory presents the possibility for designing imaging approaches that are truly optimal within the constraints of well defined performance criteria. Methods will be developed to address specific dynamic MR imaging problems. In particular we will focus on two important new applications of MRI; real-time monitoring of interventional procedures, and mapping of cerebral function.